Introduction to Digital Systems: Modeling, Synthesis, and Simulation Using VHDL

2.2 BASES AND NUMBER SYSTEMS

The objective of this section is to introduce the various types of number representations used in digital system designs. The general method for numerical representation is called positional number representation. Consider the familiar decimal system. A number in decimal representation is made of digits that range from 0 to 9. Consider the following decimal number:

This number is normally written as 4261, as the powers of 10 are implied by the position of that particular digit. Therefore, a decimal number N with n digits can be expressed as follows:

Decimal representations are said to be base-10 or radix-10 numbers because each digit has 10 possible values, weighted as a power of 10, depending on the position of the digit in the number. In a similar way, in binary representation, each binary digit has two possible values, 1 and 0, and the digits are weighted as a power of 2, depending on their position in the number. The binary system of representation is also known as a base-2 system. Consider the following binary number:

Similarly, a binary number N with n digits can be expressed as follows:

In general, any number N can be represented in a base ...